A Review of Compressive Sensing in Information Security Field

Abstract

The applications of compressive sensing (CS) in the field of information security have captured a great deal of researchers' attention in the past decade. To supply guidance for researchers from a comprehensive perspective, this paper, for the first time, reviews CS in information security field from two aspects: theoretical security and application security. Moreover, the CS applied in image cipher is one of the most widespread applications, as its characteristics of dimensional reduction and random projection can be utilized and integrated into image cryptosystems, which can achieve simultaneous compression and encryption of an image or multiple images. With respect to this application, the basic framework designs and the corresponding analyses are investigated. Specifically, the investigation proceeds from three aspects, namely, image ciphers based on chaos and CS, image ciphers based on optics and CS, and image ciphers based on chaos, optics, and CS. A total of six frameworks are put forward. Meanwhile, their analyses in terms of security, advantages, disadvantages, and so on are presented. At last, we attempt to indicate some other possible application research topics in future.

Indistinguishability and Energy Sensitivity of Gaussian and Bernoulli Compressed Encryption

“…The CS technique can also be applied in database systems [22], where random noise has been intentionally added to CS measurements for differential privacy. In practice, a variety of CS-based cryptosystems concerning the security of multimedia, imaging, and smart grid data have been suggested in [23]− [29].…”

Clustering K-SVD for sparse representation of images

“…Compressive sensing (CS) is the technique that compressively samples and reconstructs signals from fewer measurements, in order to reduce the cost of signal transmission and storage [19][20][21][22][23]. The signal x can be compressively sampled by a sensing matrix expressed as: where y ∈ R m is the measurements and ∈ R m×n with m < n. When x denotes the vectorization of an image patch, its sparse representation in terms of the dictionary D ∈ R n×q can be written as:…”

Reversible Privacy Preservation using Multi-level Encryption and Compressive Sensing

“…For instance, CSbased MRI imaging [9] or radar monitoring systems [10], [11] have been able to significantly reduce the signal acquisition time and bandwidth requirements over traditional approaches. In addition to data acquisition advantage, CS is inherently cryptographic [12], [13] since CS signals are linearly sampled using random measurement matrices. CS-based encryption runs thus in parallel with the data acquisition and is a lowcost solution compared to well-known complex encryption standards such as AES or RSA.…”